Singular Manual: weightedRing

7.5.20.0. weightedRing

Procedure from library nctools.lib (see nctools_lib).

Usage:: weightedRing(r); r a ring
Return:: ring
Purpose:: equip the variables of the given ring with weights such that the relations of new ring (with weighted variables) satisfies the ordering condition for G-algebras: e.g. \forall\;i<j\;\;lm_w(d_{ij})<_w x_i x_j.
Note:: activate this ring with the "setring" command

Example:

LIB "nctools.lib";
ring r = (0,q),(a,b,c,d),lp;
matrix C[4][4];
C[1,2]=q; C[1,3]=q; C[1,4]=1; C[2,3]=1; C[2,4]=q; C[3,4]=q;
matrix D[4][4];
D[1,4]=(q-1/q)*b*c;
def S = nc_algebra(C,D); setring S; S;
==> // coefficients: QQ(q)
==> // number of vars : 4
==> //        block   1 : ordering lp
==> //                  : names    a b c d
==> //        block   2 : ordering C
==> // noncommutative relations:
==> //    ba=(q)*ab
==> //    ca=(q)*ac
==> //    da=ad+(q2-1)/(q)*bc
==> //    db=(q)*bd
==> //    dc=(q)*cd
def t=weightedRing(S);
setring t; t;
==> // coefficients: QQ(q)
==> // number of vars : 4
==> //        block   1 : ordering M
==> //                  : names    a b c d
==> //                  : weights  2 1 1 1
==> //                  : weights  0 0 0 1
==> //                  : weights  0 0 1 0
==> //                  : weights  0 1 0 0
==> //        block   2 : ordering C
==> // noncommutative relations:
==> //    ba=(q)*ab
==> //    ca=(q)*ac
==> //    da=ad+(q2-1)/(q)*bc
==> //    db=(q)*bd
==> //    dc=(q)*cd